Automatic dead reckoning system



Sept. 26, 1961 c. BECK AUTOMATIC DEAD RECKONING SYSTEM 2 Sheets-Sheet 1 Filed Aug. 29, 1957 r ATTORNEYS C. BECK AUTOMATIC DEAD RECKONING SYSTEM sept. 26, 1961 2 Sheets-Sheet 2 Filed Aug. 29, 1957 INVENTOR cYRus BECK S I n Ix k @um z m Q Y B moho: Y m 1 F 1 IIN. .v ....y -um -lm m. 1111 1| x 1 :\lm EE .r/ N 5E: m I., Eomwm )/\o- F2. mm lm S w .El Ak! .Sa .Sl .Sa MWL Y Y flow Q L M :C im r 5E: .mm A V SL53 a ATTORNEYS nited States Patent C M' 3,001,715 AUTOMATIC DEAD RECKONING SYSTEM Cyrus Beck, 7756B Wagner Way, Elkins Park, Pa. Filed Aug. 29, 1957, Ser. No. 681,144 Claims. (Cl. 23S- 186) (Granted under Title 35, U.S. Code (1952), sec. 266) The invention described herein may be manufactured and used by or for the Government of the United States of America for governmental purposes Without the payment of any royalties thereon or therefor.

The present invention relates to an automatic dead reckoning system and more particularly to an automatic dead reckoning system in which the polar forms of the various velocity vectors are combined and integrated upon directly to compute instantaneous positional information.

Present arrangements for use aboard carrier-based aircraft to determine aircraft position relative to the carrier generally utilize techniques in which the various velocity vectors of carrier, Wind, and aircraft are rst resolved into their N-S and E-W components, added, and the sums of the components individually integrated and then converted back into the polar form by` means of resolvers to give the instantaneous ground distance and direction or bearing of the airplane with respect to its carrier. These techniques require elaborate apparatus for accomplishing the resolution of the various vectors into their components and their recombination, and lead to nudesirable inaccuracies as well as increased weight and cost.

The present invention overcomes the aforementioned disadvantages of prior arrangements by resorting to direct integration of the polar vectors Without the intermediateV steps of resolution and recombination. Based upon a succinct mathematical statement of the various Vectors inv olved, a novel null-seeking analog computer is provided for receiving all of the various inputs and producing automatically the final distance vector completely defined for indicating the distance and angle between the moving craft and moving point of reference. The system, although particularly adaptable for use with an aircraft based on an aircraft carrier, can also be adapted for use wherever a plurality of vectors are to be combined and then integrated, or a single, varying vector is to be integrated.

It is an object of the present invention to provide apparatos for automatically computing from velocity vectors the ground distance and direction of an aircraft from afixed or moving point of reference.

A further object is the provision of simple apparatus for solving and integrating a plurality of vectors without departing from their polar form.

Another object of the invention is the provision of apparatus for performing direct integration on a continuously varying vector in the polar form.

Other objects and features of this invention will become apparent from consideration of the following specification relating to the annexed drawings in which:

F16. l shows a velocity vector diagram relating to an aircraft operating from a moving aircraft carrier.

FIG. 2 illustrates schematically an automatic dead reckoning system according to the principles of this invention for application to the situation illustrated in FIG. l,

FIG. 3 shows one detail of the dead reckoning system of FIG. 2.

FIG. 4 illustrates a special case of the invention.

When an aircraft departs from its carrier base, a vector diagram such as that shown in FIG. l illustrating speed and heading of the carrier Patented Sept. 26, 1961 v wind velocity and direction (Vw) and aircraft speed and heading (Vs) will permit calculation of the closing vector M M @5A then by De Moivres theorem,

(2) eA- ecos A+i sin A Under the particular circumstances outlined above,

Vbe5b=velocity vector of the moving carrier, Where b is the angle with respect to the reference direction;

Vea=t`rue airspeed vector, Where a is thhe angle with' respect to the reference direction; Vwew=wind speed vector, where w is the angle With re spect to the reference direction; and Vmemw-closing or velocity of moving carrier relative to airplane from FIG. l at an angle m to the reference direction.

Stated mathematically, the vector diagram of FIG. l`

is described as follows:

(3 Vbeb-l- Vaea-l- Vwew: Vmem in which terms Vaeja and VweW are negative.

If the distance vector from the airplane to the carrierl is Rel", where R and 6 are respectively the range and ground track angle from the aircraft to the carrier Substituting (3) into (4) gives Putting the left side of (6) in Cartesian from by utilizing the expansion of (2).

Vb sin (b-e)-V, sin (a--V.. sin (tu-@mrtg provide the solution for R and 6 desired.

An automatic dead reckoning system built according to the principles of this invention Will solve Equations 8, 9, Iand 10, simultaneously. .As-illustrated in FIG. 2, the system includes the input units l0, 12 and i4 which are each designed to receive one of the various input parameters noted above. Each of the input units 10, 12, and 14 are interconnected by a mechanical linkage or coupling arrangement 11 which is schematically shown by dotted lines. For example, unit 10, which `is shown more particularly in FIG. 3, consists of a pair of potentiometers 16 and 18 having wipers 16' and 18', respectively, a resolver 20, and a mechanical differential 21. Wipers i6' and I8' are positioned in unison by a connection 22 in accordance with carrier speed Vb either manually by a dial (not illustrated) or some other automatic apparatus not forming a part of this invention. Resolver 2li consists of a pair of stationary, right angularsecondary coils 23V and 25, and a rotatable primary coil 24 which is excited by some power source such as 400 c.p.s., 110 volts, as is understood in the art. Rotor 2-4 is positioned at bby the output shaft 26 of differential 21 into which is fed shaft positions b representing the heading of the carrier =and representing the return heading of the aircraft tovbe determined by the illustrated system. Heading b, like speed Vb of the carrier, may be manually or autoinatcallv supplied, While angle a is 4ted back through a mechanical connection from elsewhere in the system, as described below.

. Hence, it will be seen that wiper 16' ,on potentiometer 16 will pick ot a voltage for line-3l having the magnitude Vb cos (bf), while wiper 1,8 on potentiometer A18 select a voltage for line 32 having the magnitude Yv3, 'sin (lv-0).

Units 12 and 1,4 which are similarly constructed to accept the parameters dealing with airplane speed and heading, and wind speed and direction; respectively, produce on lines 33, ,34, 35 and 36 the information indicated in FIG. 2. VFor this purpose, unit l2 Vconsists oi the potentiometers 40 and 42, a resolver 44, and a mechanical dinerential 45 while unit t4 consists of pctentiometers te and 48, a resolver 50, and a mechanical Vdiierential l.

The outputs Vb cos (l2-0), Vb cos (cz-6), and Vw cos Y (w--6) of potentiometer-s 16, 40 and 46, respectively,

forming one side of Equation 8 are passed through the summing amplier 52 to be vcombined ifo-accordance with the signs given in Equation 8 to obtain the output voltage ai "di which is proportional to the algebraic sum of all the components entering into the rate of change of the ground range R, is then passed into the integrator or integrating ampliier Y54 for producing a signal representing R, which is lthe magnitude of the iinal vector or distance desired,

as explained above, and energizes a voltage meter 56 for a direct indication of this value.

The outputs Vb sin (li-0), Va sin (a-9), and VW sin (w-0) from potentiometersll, 42 and 4 8, respectively, forming the terms Von one side of Equation 9, are passed to the summing amplifier 58 for producing the output voltage @-6 Y Y di which is passed to an integrator 59. The term represents a lvoltage proportional to the algebraic sum of all the sine terms or components entering into the rate of change of the azimuth angle 6.

A pair of potentiometers 60 and 62 are provided to receive across ground the outputs n di trom amplier 52 and R from integrator 54, respectively. i

as provided in Equation 10, while summing amplier 74 accepts the output 0R from integrator 59 and mixes it in opposition to 0R from potentiometer 62. The output signal from ampliiier 74 is therefore nulled whenthe inputs thereto from potentiometer 62 and integrator 59 are equal. Servo motor 76 is accordingly driven by the output of amplifier 74 in the direction of cancelling or milling che input thereto by means of the mechanical coupling arrangement 11 to which it is drivingly connected. Hence, the whole system will stabilize itself at some null position and readjust itself continuously with changing conditions to maintain the shaft of motor 76 and hence the mechanical coupling 11 at some position representing angle 0, which is recorded on a meter 78 that measures the. angular displacement of the .coupling 11 for view by the pilot or operator. It will be seen that the angle 0 as indicated on meterA 78 representing the heading or direction of vector R is the only value that will satisfy' all the Equations 8, 9 and l0. Y

In the operation of the system described above, the operator would by manual or automatic means feed in the values of Vb, Vb, Vw and angles b, a and w, as noted above. The system thereafterwould rebalance -it-self to -a null position, motor 76 being driven by the output of amplier 74 for this purpose. This establishes a stable Y value R and angle 9, as indicated on meters 56 and 7S,

respectively. Of course, it is understood that the values of Vthe vectors both magnitude and angularwise may be changed periodically either manually by the operator or automatically in accordance with other apparatus known in the art and not forming a part of this invention. Thus, at all times the values of R and 0 would be available for indicating the instantaneous distance and bearing back to the carrier. l

It is seen that the apparatus described above and illustrated in FIG. 2 provides for directly summing and integrating three vectors in their polar form. if two of the three vectors were reducedto, and maintained at zero, then the system lwould effectively provide for the continuous integration with respect tok time or" a variable` 'velocity vector to obtain the total straight line distancev i 5 system' would have the configuration illustrated AinFIG. 4. Vector VX having a polar angle x is the vector undelgoing integration with respect to time. Unit v will de 'ver since the other additive terms of Equations 8 and 9 are zero. These signals are supplied directly to integrators 54 and 59, and potentiometer 60. The remainder of the system is identical to that shown in FIG. 2, with R and shown by meters 56 and 78, respectively.

A. Furthermore, without departing from the principles of this invention, the number of vectors or input parameters may be increased by adding units similar to 10, 12 and 14 to the coniiguration of FIG. 2 for each added vector. The signs of the various additive terms in Equations 8 and 9 would depend upon physical conditions necessitating that the summing amplifiers and integrators be connected to accomplish the adding and subtracting, as neces sary. These components are well known in the art and maybe selected to meet existing loads and conditions.

lt is thus seen that' applicant has provided not only novel navigational apparatus, but a unique servo system for general use in vector addition and simultaneous integration of the variety hereinbefore described.

It should be understood of course that the foregoing disclosure relates to only preferred embodiments of this invention yand that numerous modifications or alterations thereof may be made therein without departing from the spirit and the scope of the invention as set forth in the appended claims.

What 'is claimed is:

l.' A'self-balancing servo system operating in response to a plurality of inputs each of which is a vector of par- L tieular magnitude Iand direction, comprising, in combination, servo motor means having a irst shaft angular position, differential means for each of said vectors con.- nected to said servo motor means and producing a second shaft angular position which 4is the 'alger-braio dif- Iference between the particular vector directions'and said first shaft angular position, resolver means havmg input means connected to each said diierential means for producing a' pair of sine and cosine voltage outputs forV each of said vectors as a function of each respective second shaft angular position, means multiplying each of said sine and cosine outputs bythe magnitude of each respective vector producing a plurality of sine vand cosine vol-tage terms and providing a proportional voltage out-f put, means -for summing each of said cosine terms and. providing a proportional voltage output, means for .summing each of said sine terms and providing a proportional voltage output, first integrator means `for integrating the output of said cosine summing means, means also multiplying the output of said cosine summing means by said rst shaft angular position producing a rst output voltage, means multiplying the output of said first integrating means also by said :first shaft angular position. producing la second output voltage, second integrating means for integrating the sum of said iirst output voltage and the output of said sine summing means, and servo ampliiier means yfor amplifying the difference between said second output voltage and the output of said secondV integrating means for driving said servo motor means in the direction of cancelling said difference.

2. A self-balancing servo system for integrating with respect to a function t the polar vector having a magnitude V and a direction x both varying with respect to said function t, comprising, in combination: servo motor means having a null position 9; meam connected to said servo motorv means for producing ia pair of signal voltages V cos (x-G) and V sin (x-); rst potentiometer means for converting signal voltage V cos (ac-0) into a voltage 0V cos (Jr-6); iirst integration means for integrating with respect to function t, the sum of signal voltage (V sin (x-) and 6V cos (2o-6) and obtaining a iirst voltage 0R; second integrating means for integrating the signal voltage V cos (x-) and obtaining a voltage R; second potentiometer means for converting signal voltage R into a second voltage 6R; and servo amplifier means responsive to the diiference between said first and second voltages 6R and connected to [and driving said servo motor means in the direction of reducing said difference to zero, said voltage R being the magnitude and 0 the direction of the resultant Vector after said integration.

3. A self-balancing servo system operating in response to a plurality of inputs each of which represents a Vector of particular magnitude and direction, comprising, in combination, servo motor means having a shaft angular' position, means including diierential and resolver means for producing for each input vector a pair of sine and cosine voltage outputs as a function of the algebraic diifen' ence between the particular vector direction and said shaft output angular position multiplied by the magni* tude of each respective vector and producing a plurality of sine and cosine voltage terms, said servo motor means being connected to said dierential means, means for summing each of said cosine terms and providing a proportional voltage output, means for summing each of said sine terms and providing a proportional voltage output means for integrating and multiplying by said shaftangular position the output of said cosine summing means producing a iirst output voltage, means integrating the sum of the output of said sine summing means and the.' output of said cosine summing means, the latter output being iirst multiplied by said shaft angular position, said integrating means producing a second output voltage, and servo amplifier means for amplifying the difference between said first and second output voltages for driving said servo motor means in the direction of cancelling said difference.

4. A self-balancing servo system operating in response to a plurality of inputs each of which is a vector of particular magnitude and direction, comprising, in combination, servo motor means having a shaft angular position, means including differential and resolver means for' producing for each input vector a -pair of sine and cosine voltage outputs as a function of the algebraic diierence between the particular vector direction and said shaft.

output angular position multiplied by the magnitude of each respective vector and producing a plurality of sine and cosine voltage terms, said servo motor means being connected to said differential means,V means for summing each of said cosine terms and providing a proportional voltage output, first integrator means for integrating the: output of said cosine summing means, means also for multiplying the output of said cosine summing means by said shaft angular position producing a rst output volt-' age, means multiplying the output of said first integrating means also by said angular position producing a second output voltage, second integrating means for integrating the sum of said iirst output voltage and the output of said sine summing means, and servo amplifier means for amplifying the difference between said second output voltage' and the output voltage of said second integrating meansl motor means being connected to said derential means, resolver means having input means connected to said diiferential means for producing for each of the latter means a pair of sine and cosine voltage outputs as a functionof each respective second shaft output angular position multiplied by the magnitude of each respective vector and producing a plurality of sine and cosine voltage terms, means for summing each of said cosine terms and` providing a proportional voltage output means for summing each 0f said sine terms and providing a proportional voltage output means for integrating and multiplyingV by said first shaft angular position the output of said cosine summing means producing a first outputV voltage, means integrating the sum of the output of said sine summing means and the output of said cosine summing means multiplied by said lirst shaft angular position producing a second output voltage, and servo amplifier means for amplifying thedilerence between said rst and second output vvoltages for driving said servo motor means inthe direction of canceling said difference.

6,. A selfsbalancing servo system operating in response to a plurality of inputs each of which is a vector of particular magnitude and direction, comprising, in combination, servo motor means having a first shaft angular position, differential means connected to said servo means and producing for each of said vectors a second shaft angular position which is the algebraic dilerence between the particular vector direction and said first shaft angular position, receiver means connected to said dierental means for producing for each of the latter means a pairof sine and cosine voltage outputs as a function of each respective second shaft angular position, means multiplying each of said sine and cosine outputs by the magnitude of each,v respective vector and producing a plurality or sine and cosine voltage terms, means for summing each of' said cosine terms and providing a proportional voltage output means for summing each of said sine terms and providing a proportional voltage output, rst integratorV means for integrating the output of said cosine summing means, means also multiplying the output of said cosine summing means by said rst shaft angular position producing a first output voltage, means multiplying the output of said rst integrating means also by said rst shaft position producing a second output voltage, second integrating means for integrating the sum of said rst output voltage Vand the output of said sine summing means, and servo amplifier means for amplifying the difference between said second output voltage and the output voltage of said second integrating means for driving Vsaid servo motor means in the direction of canceling said difference, Y

7. Av self-balancing servo system operating in response to a plurality of inputs each of which is a vector of particular magnitude and direction, comprising, in combinat tion, servo motor means having a first shaft angular position, a plurality of differential means connected to the output shaft of said servo motor means, means producing for each of said' vectors a second shaft angular position which is the algebraic difference between the particular vector VdirectionV and said lirst'sh-af-t angular position, resolver means each having a rotor driven by one of said differentialA means for producing for each of the latter means a pair 0f sine and cosine voltage outputs as a function of each respective second shaft output angular position, potenti- (mieter means multiplying each of said sine and cosine outputs by the magnitude of each respective vector and producing -a plurality of sine and cosine voltage terms, means for summing each of said cosine terms and providing a proportional output voltage means for summing each of said sine terms, and providing a proportional out# put voltage, rst integrating means for integrating the output of said cosine summing means, means also multiplying the output of said cosine summing means lby said lrstV shaft angularfposition producing a first output voltage, means multiplying the output of said `rst integrating 't y i 8 v means also by said rst shaft angular position yproducing a second output voltage, second integrating means for ntegrating the'sum of said rst output voltage and the output of said sine summing means, and servo amplier means for amplifying the difference between said second output voltage and the output of said second integrating means for driving said servo motor means in the direction of cancelling said difference.

8. A self-balancing servo system for combining a plurality of independently variable vectors each characterized by a magnitude V anda direction represented by x with respect to a reference direction and integrating the resultant thereof to produce Ya nal'vector of determined magnitude and direction, comprising, in combination. servo motor means having a null shaft angular position 0, resolver and differential means for each of said vectors operating on inputs V, x, and said null shaft position 6 for producing a rst output voltage V cos (Je-'0) and a second output voltage V sin (x-0) for each of said vectors, said diterential means being connected to said' servoV motor means; means for receiving said rstoutput voltages and producing a voltage dR Y d: Y

representative of the sums of said rst output voltages of said vectors; means for receiving said second output v'oltages and producing a voltage d6 Rat representative of the product of voltages representative of dR TIT and 6; rst integrator means for integrating said voltages and delivering a rst voltage HR; second integrator means for operating on said voltage and producing a voltage R representative ofthe magnitude of the nal vector means for multiplying said voltage R by .an electrical quantity representative of angle 6 andv producing a second voltage designated as 0R; and servo amplifying means for -amplifying the diierence between said rst and second voltages 6R and driving said servo motor and said differential means in the direction of reducing said difference to zero and balancing at said null shaft position 0.

9. A self-balancing servo system oper-ating in response: to a plurality of inputs of each of which is a vector of particular magnitude V and direction x, comprising, in combination, servo motor means having au instantaneous shaft angular position 6, Ydifferential means connecting to said servo motor means andmeans producing for each of said vectors a shaft output angular position which sthe algebraic difference between 9 and x, resolver means responsive to the latter said angular position for producing for each vector a pair of sine and cosine voltage outputs V sin (x-) and V cos (x-), means for summing each of said cosine terms and providing a proportional voltage output, means for summing each of said sine terms and providing a proportional voltage output, means for integrating and multiplying by `an electrical quantity repre sentative of the angle 6 the output of said cosine summing means producing a rst output voltage designated as 6R, means integrating the output of said sine summing means and the output of said cosine summing means multiplied by an electrical quantity representative of the angle 0 for producing a second output voltage also designated as 0R, and servo ampliiier means for amplifying the difference between said first and second output voltages for driving said servo motor means in the direction of cancelling said diierence.

10. A dead reckoning navigational system for computing the straight-line distance and direction of an aircraft relative to a moving reference point comprising, in combination: servo motor means having a null shaft angle position 0; diierental and resolver means responsive to reference point heading b, reference point speed Vb, and 0 for producing a pair of output voltages Vb cos (b-) and Vb sin (b-); differential and resolver means responsive to wind direction W, wind speed Vw, and 0 for producing a pair of output voltages Vw cos (w-H) and Vw sin (w-); differential and resolver means responsive to aircraft heading a, aircraft speed Va, and 6 for producing ya pair of output voltages V, cos (zz-0) and Va sin (Lz-0); all of said differential means being oonnected to said servo motor means; first summing means for summing the output voltages Vb cos (b-), V, cos (a--6), and Vw cos (w-) for producing an output voltage designated as second summing means for the output voltages 10 Vb sin (I1-0), V, sin (zz-0), and VW sin (w-9) for producing an output voltage designated as first integrating means for integrating said voltage with respect to time and producing a voltage R proportionate to the distance between the aircraft and the moving reference point; means also separately multiplying said output voltage by an electrical quanti-ty representative of the angle 0 and producing a first voltage designated as R0; means for summing an integrating d6 dR R tlld @E and producing a second voltage also designated as 0R; and servo amplifier means for amplifying the diierence between said irst and second voltages 0R for driving said servo motor means in the direction of cancelling said difference, said voltage R representing said straight-line distance and 0 the direction thereof.

References Cited in the le of this patent UNITED STATES PATENTS 2,536,495 Ewing Jan. 2, 1951 OTHER REFERENCES Electronic Instruments (Rad. Lab., vol. 21), by Green- Wood et al., McGraw-Hill, New York, 1954.

Control Engineering, vol. 1, No. 3, November 1954 (31 Ways to Multiply, by S. A. Davis), pp. 45 and 46 relied on.

UNTED STATES PATENT @FFME CERfIFICATEA 0F CGRBECTIQN Patent No. 3,001,715 September 26, 1961 Cyrus Beck It s hereby certified that error appears in the above numbered pat ent requiring correction and that the Said Letters Patent should 'ead as corrected below.

Column 2, line 29, for "thhe" read the line 56, for "frem" read form column 8, line 70, strike out "of", flrst occurrence; line 73, for "conmecting'.l read connected Signed and sealed this 14th day 0f August 1962.

(SEAL) DAVID L. LADD Atmung officer 

